Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17984861 | C2 | semidirect |
| 2. #22581501 | C2 | semidirect |
| 3. C4×#14555784 | C2 | semidirect |
| 4. #22581174 | C2 | semidirect |
| 5. #22581166 | C2 | semidirect |
| 6. #22581164 | C2 | semidirect |
| 7. #22581158 | C2 | semidirect |
| 8. #22581150 | C2 | semidirect |
| 9. C4⋊C8×D139 | C2 | semidirect |
| 10. #22580946 | C2 | semidirect |
| 11. #459×C139 | C2 | semidirect |
| 47. #14555784 | D4 | semidirect |
| 135. C4×C139 | #135 | semidirect |
| 150. C139 | #3035 | semidirect |
| 160. #459 | D139 | semidirect |
| 292. C4 | #17984861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984861 | 2 |
| #22581501 | 2 |
| C4×#14555784 | 2 |
| #22581174 | 2 |
| #22581166 | 2 |
| #22581164 | 2 |
| #22581158 | 2 |
| #22581150 | 2 |
| C4⋊C8×D139 | 2 |
| #22580946 | 2 |
| #459×C139 | 2 |
| #3035 | 139 |